class Solution {
public:
    int minFallingPathSum(vector<vector<int>>& matrix)
    {
        int n = matrix.size();
        vector<vector<int>> dp(n + 1, vector<int>(n + 2, INT_MAX));
        for (int i = 0; i <= n + 1; i++)dp[0][i] = 0;

        int ret = INT_MAX;
        for (int i = 1; i <= n; i++)
        {
            for (int j = 1; j <= n; j++)
            {
                dp[i][j] = min(min(dp[i - 1][j], dp[i - 1][j - 1]), dp[i - 1][j + 1]) + matrix[i - 1][j - 1];
                if (i == n)ret = min(dp[i][j], ret);
            }
        }
        return ret;


    }
};